D3 branes in a Melvin universe: A new realm for gravitational holography

Abstract

The decoupling limit of a certain configuration of D3 branes in a Melvin universe defines a sector of string theory known as Puff Field Theory (PFT) -a theory with non-local dynamics but without gravity. In this work, we present a systematic analysis of the non-local states of strongly coupled PFT using gravitational holography. And we are led to a remarkable new holographic dictionary. We show that the theory admits states that may be viewed as brane protrusions from the D3 brane worldvolume. The footprint of a protrusion has finite size -the scale of non-locality in the PFT -and corresponds to an operator insertion in the PFT. We compute correlators of these states, and we demonstrate that only part of the holographic bulk is explored by this computation. We then show that the remaining space holographically encodes the dynamics of the D3 brane tentacles. The two sectors are coupled: in this holographic description, this is realized via quantum entanglement across a holographic screen -a throat in the geometry -that splits the bulk into the two regions in question. We then propose a description of PFT through a direct product of two Fock spaces -akin to other non-local settings that employ quantum group structures. 1 jfreedbrown@hmc.edu 2 vkhemani@hmc.edu 3 sahakian@theory.caltech.edu arXiv:0910.0073v3 [hep-th] 17 May 2010 4 For other realizations of branes in Melvin backgrounds, see [22]-[25]

From surface operators to non-Abelian volume operators in puff field theory

“…And the bulk space has two sectors, one for describing puff dynamics at wavelengths larger than their size, and another for the internal degrees of freedom of puffs. The two sectors also appear quantum entangled [30]. In general, the concluding picture shown in Figure 1 is obviously reminiscent of defects arising in local gauge theories.…”

“…In previous works, Wilson lines have been shown to play a particularly important role in understanding novel non-local gauge invariant features of such theories [23,24,25]. The purpose of this work is to use surface operators to explore a particular scaling regime of string theory known as Puff Field Theory [26]- [30].…”

“…On the other hand, one has decent computational handle on the strong coupling regime of the theory through the holographic dual geometry constructed in [27]. In [30], this geometry was probed using geodesics and evidence was presented that the PFT puffs may be the footprints of D3 brane tentacles or protrusions inserted onto the PFT worldvolume, as cartooned in Figure 1. Non-local operator insertions get inserted in the bulk instead of the boundary -at an extent related to their puff size as determined by the UV-IR correspondence.…”

“…These include generators of the U (1)×U (2) R-symmetry group of the dual PFT. We have four such generators given by [30] K 0 = ∂ χ ;…”

“…Note that, at the singularity ψ = π/2, this screen is pushed deep into the UV. In [30], it was also pointed out that this screen appears to split the holographic bulk into two regions, with both sides projecting onto the common boundary at w H : it was proposed that the side with small w holographically encodes dynamics of the non-local states at lengths greater than their puffed-up size; while the large w region encodes the internal dynamics of the puffs. This picture makes sense if we are to view the non-local states as footprints of D3 brane protrusions into the bulk.…”